cp's OEIS Frontend

A130543 Multiplicative persistence of n!.

%I A130543 #14 Jul 18 2024 04:36:44
%S A130543 0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A130543 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A130543 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A130543 Multiplicative persistence of n!.
%C A130543 From 5! on all the factorials end with "zero" thus the persistence is equal to 1.
%C A130543 Decimal expansion of 1/90000. - _Elmo R. Oliveira_, May 05 2024
%H A130543 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A130543 From _Elmo R. Oliveira_, Jul 16 2024: (Start)
%F A130543 G.f.: x^4/(1-x).
%F A130543 a(n) = 1 for n >= 4.
%F A130543 a(n) = 1 - A329678(n) = A185115(n+1). (End)
%e A130543 0!=1; 1!=1; 2!=2; 3!=6 --> Persistence=0
%e A130543 4!=24 --> 2*4=8 --> Persistence=1
%e A130543 5!=120 --> 1*2*0=0 --> Persistence=1
%p A130543 P:=proc(n)local i,k,w,ok,cont; for i from 0 by 1 to n do w:=1;k:=i!;ok:=1; if k<10 then print(0); else cont:=1; while ok=1 do while k>0 do w:=w*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if w<10 then ok:=0; print(cont); else cont:=cont+1; k:=w; w:=1; fi; od; fi; od; end: P(100);
%Y A130543 Cf. A031346, A130544, A185115, A329678.
%K A130543 easy,base,nonn
%O A130543 0,1
%A A130543 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 04 2007